Spectroscopic analysis makes use of a change in the properties of energy, such as light, after it interacts with a material sample. For example, the property of light most often correlated to a property of the sample is the intensity of the light. According to the Beer-Lambert law, the intensity of light transmitted through a samples varies exponentially with respect to the absorptivity of the sample (usually expressed as molar absorptivity or molecular absorptivity), the path length through which the light is transmitted, and the concentration of the absorbing species in the sample such that I(λ)/I0(λ)=exp(L*E(λ)*C(molecule specific)), where I and I0 represent the intensity before and after entering the sample, respectively, and where L is the optical path length, E(λ) is the absorptivity, and C is the concentration of the sample.
Due to the exponential relationship, this law is often expressed in logarithmic form as log(I/I0)=LEC (a wavelength and molecule specific form), or −Log(I/I0)=Log(I0/I)=A, where A is the adsorption, or Log(1/I)=optical density. For adsorption, it is assumed that the attenuation is due entirely to the absorption of photons by molecular species, whereas the optical density (OD) formulation does not make this assumption. Attenuation due to scattering may also cause a reduced intensity of transmitted light, however this relationship is also logarithmic and therefore the functional form of the Beer-Lambert law continues generally to be effective.
Thus, the Beer-Lambert law can serve to relate sample absorption to a chemical or physical-chemical property (physical properties that correlate with chemical properties) of the sample. However, it should be noted that while the law is founded on first principles and operates over a large range of E*C values, most analysis instruments do not. That is, to increase their dynamic range, different optical path lengths (L) are used to optimize response. These lengths are typically obtained by physically adjusting some arrangement of analyzer parts over a specific range, to change the path length of light transmitted through a sample. In addition, for high values of E*C, the law breaks down. Nonlinear calibration curves to extend analyzer dynamic range in these situations may be used.